Inequalities and Quantum Entanglement
From the Cauchy-Schwarz Inequality to Non-linear Entanglement Witnesses
S.M. Loor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J Vermeer – Mentor (TU Delft - Analysis)
D. Elkouss – Mentor (TU Delft - Quantum Information and Software)
C Vuik – Graduation committee member (TU Delft - Numerical Analysis)
Tim H. Taminiau – Graduation committee member (TU Delft - QID/Taminiau Lab)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this thesis, two topics are studied: mathematical inequalities and non-linear quantum entanglement witnesses. First, various inequalities, like the Cauchy-Schwarz inequality (on finite dimensional vector spaces) and Jensen's inequality, along with their extensions and generalisations, are proved and discussed. The intimate relationship between these inequalities is studied. Because this thesis was restricted to finite dimensional vector spaces, the consequences of generalising the results to infinite dimensional vector spaces are finally determined. Secondly, the topic of entanglement detection is discussed - specifically, non-linear entanglement witnesses are considered. A bipartite and multipartite entanglement criterion based on the previously discussed inequalities are introduced and assessed extensively by considering their optimality, how they relate to other criteria as well as their limitations.